PITTSBURGH — Federal prosecutors said this morning that the West Penn Allegheny Health System has agreed to pay more than $1.5 million to settle claims that it violated the law by offering doctors below-market rents so the physicians would refer patients to the network’s hospitals.

A spokesman for West Penn says the settlement grew out of a self-audit and voluntary report made to federal officials, which was confirmed by U.S. Attorney David Hickton, who announced the settlement. The allegedly illegal activity began in the mid-2000s, with most of it occurring between 2008 and 2012.

That was before Pittsburgh-based health insurer Highmark Inc. bought the five-hospital West Penn network and created the Allegheny Health Network with two other hospitals it has acquired.

West Penn had experienced financial difficulties before the Highmark takeover.